The American Godzilla vs a Nuke, well let's consider the following aspects of a Nuke.
1: High force, particularly at the "ground zero"
2: Extreme Heat
3: Nuclear Radiation
Now several critters, such as certain insects and microbes, have shown to be resiliant or unharmed by Nuclear Radiation. The American Godzilla may even use it as fuel for its Atomic Breath.
A chemist called Maurice Ward (died in 2011) created a material called Starlite could withstand the temperature of even a Nuclear bomb. The test, for example, had it wrapped around an egg with a flamethrower blowing on it. After the several minute blast the Starlite was removed... and the egg was room temperature! It's possible for the American Godzilla to have a heat resiliance so high that even a Nuke's heat wouldn't be a threat. Deep sea critters that thrive at hydrothermal vents have to be able to withstand some 600 degrees (Fahrenheit) so it's possible.
Now the extreme pressure, considering the American Godzilla's armored hide, it's possible even this wouldn't hurt Godzilla. Now I don't know the full strength of the armor for that info hasn't been released yet. For realism, a tough yet light armor is realistic as opposed to the super speed regeneration.
Now a nuke could get kill Godzilla if it exploded in its stomach. Though how do you sneak a Nuke in there would be a 'Mission Impossible' task alone.
I believe in Jesus Christ, who's my Lord and Savior.
John 3:16, Job 41:1-34, Leviticus 18:22